Answer:
29273.178 joules have been added to the gas for the entire process.
Explanation:
The specific heats of monoatomic gases, measured in joules per mol-Kelvin, are represented by the following expressions:
Isochoric (Constant volume)
(1)
Isobaric (Constant pressure)
(2)
Where 
is the ideal gas constant, measured in pascal-cubic meters per mol-Kelvin.
Under the assumption of ideal gas, we notice the following relationships:
1) Temperature is directly proportional to pressure.
2) Temperature is directly proportional to volume.
Now we proceed to find all required temperatures below:
(i) <em>Alice heats the gas at constant volume until its pressure is doubled</em>:
(3)
(
, 
)
(ii) <em>Bob further heats the gas at constant pressure until its volume is doubled</em>:
(4)
(
, )
Finally, the heat added to the gas (
), measured in joules, for the entire process is:
![Q = n\cdot [c_{v}\cdot (T_{2}-T_{1})+c_{p}\cdot (T_{3}-T_{2})]](https://tex.z-dn.net/?f=Q%20%3D%20n%5Ccdot%20%5Bc_%7Bv%7D%5Ccdot%20%28T_%7B2%7D-T_%7B1%7D%29%2Bc_%7Bp%7D%5Ccdot%20%28T_%7B3%7D-T_%7B2%7D%29%5D)
(5)
If we know that 
, 
, , and , the heat added to the gas for the entire process is:
![Q = (2\,mol)\cdot \left[\left(12.471\,\frac{J}{mol\cdot K} \right)\cdot (536.3\,K-273.15\,K)+\left(20.785\,\frac{J}{mol\cdot K} \right)\cdot (1092.6\,K-546.3\,K )\right]](https://tex.z-dn.net/?f=Q%20%3D%20%282%5C%2Cmol%29%5Ccdot%20%5Cleft%5B%5Cleft%2812.471%5C%2C%5Cfrac%7BJ%7D%7Bmol%5Ccdot%20K%7D%20%5Cright%29%5Ccdot%20%28536.3%5C%2CK-273.15%5C%2CK%29%2B%5Cleft%2820.785%5C%2C%5Cfrac%7BJ%7D%7Bmol%5Ccdot%20K%7D%20%5Cright%29%5Ccdot%20%281092.6%5C%2CK-546.3%5C%2CK%20%29%5Cright%5D)
29273.178 joules have been added to the gas for the entire process.
